How do you solve #5x ^ { 2} - 9x < - 4#?

1 Answer
Mar 26, 2018

#4/5 lt x lt 1#

Explanation:

We have,

#color(white)(xxx)5x^2 -9x lt -4#

#rArr 5x^2 -9x +4 lt 0# [Transpose #-4# to L.H.S.]

#rArr 5x^2 -5x -4x + 4 lt 0# [Break #-9x# as #-5x -4x#]

#rArr 5x(x - 1) - 4(x - 1) lt 0# [Group the like terms]

#rArr (x -1) (5x -4) lt 0# [Group again]

Now for the inequality to be true,

Either #(x - 1) lt 0# or #(5x - 4 ) lt 0#

So, Either #x lt 1# or #x lt 4/5#

If #x lt 4/5#, then it is automatically #lt 1#. Then, Both Term will be negative. So, It can't be possible.

So, The interval of values for #x# is :- #4/5 lt x lt 1#

Hence Explained.